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arXiv · 2001.09626

A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers

Michal Bosy·Monica Montardini·Giancarlo Sangalli·Mattia Tani
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Abstract

In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit the tensor product structure at the patch level. To this purpose, we extend to the isogeometric framework the so-called All-Floating variant of FETI, that allows us to use the Fast Diagonalization method at the patch level. We construct then a preconditioner for the whole system and prove its robustness with respect to the local mesh-size $h$ and patch-size $H$ (i.e., we have scalability). Our numerical tests confirm the theory and also show a favourable dependence of the computational cost of the method from the spline degree $p$.

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Michal Bosy, Monica Montardini, Giancarlo Sangalli, Mattia Tani. 2020-01-27. A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers. https://doi.org/10.1016/j.camwa.2020.08.024

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